Coordinate systems and analytic expansions for three-body atomic wavefunctions. II. Closed form wavefunction to second order in r
JE Gottschalk, PC Abbott… - Journal of Physics A …, 1987 - iopscience.iop.org
JE Gottschalk, PC Abbott, EN Maslen
Journal of Physics A: Mathematical and General, 1987•iopscience.iop.orgFor pt. I, see ibid., vol. 20, no. 8, p. 2043-75 (1987). Several coordinate systems for solving
the few-electron Schrodinger equation are presented. Formal solutions corresponding to
each coordinate system are given in terms of the Fock expansion and their interrelationships
and general structure are examined. Attention is focused on the solutions obtained using
spherical polar coordinates for a Coulomb potential of arbitrary symmetry. The wavefunction
is obtained up to second order in the hyperradius r=(r 2 1+ r (sup) 2 2) 1 2/, and the special …
the few-electron Schrodinger equation are presented. Formal solutions corresponding to
each coordinate system are given in terms of the Fock expansion and their interrelationships
and general structure are examined. Attention is focused on the solutions obtained using
spherical polar coordinates for a Coulomb potential of arbitrary symmetry. The wavefunction
is obtained up to second order in the hyperradius r=(r 2 1+ r (sup) 2 2) 1 2/, and the special …
Abstract
For pt. I, see ibid., vol. 20, no. 8, p. 2043-75 (1987). Several coordinate systems for solving the few-electron Schrodinger equation are presented. Formal solutions corresponding to each coordinate system are given in terms of the Fock expansion and their interrelationships and general structure are examined. Attention is focused on the solutions obtained using spherical polar coordinates for a Coulomb potential of arbitrary symmetry. The wavefunction is obtained up to second order in the hyperradius r=(r 2 1+ r (sup) 2 2) 1 2/, and the special case of 1 S states is then reduced to a closed form using classical techniques. The insight gained from this reduction suggests methods for solving the wavefunction to all orders. The results hint at the existence of closed form wavefunctions for few-body systems.
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